# Federal Funds Rate Predictions

## Binary Options

### Binary Overview

On July 12, 2006, the Chicago Board of Trade (CBOT) launched a binary option on the target federal funds rate. The new option is binary in the sense that there are only two payouts at expiry: $1,000 or $0. An expiring option is cashed settled on the last day of a regularly scheduled Federal Open Market Committee (FOMC) meeting, after the target rate is announced. The payout amount is based on the relationship between the option’s strike price and the target federal funds rate (quoted in terms of 100 minus the interest rate) set by the FOMC. For options that expire in the money, long-position holders receive $1,000, and short position holders pay $1,000. Contracts that cover the next four FOMC meetings are traded. For more contract details, see: “Binary Option Specs,” CBOT Web site.

The binary option differs from the CBOT’s option on the 30-day fed funds rate in some important ways. Thanks to carefully conceived specifications, the new instrument offers an alternative and more direct means of assessing market opinion on the probabilities of alternative future FOMC target rate choices.

The most important difference between the new binary options and the options on federal funds futures is that the underlying on the new contract is the target federal funds rate itself, rather than the monthly average federal funds rate. Thus, when using the binary options to recover probabilities associated with potential target rates, there is no need to keep track of day counts before and after an FOMC meeting and no need to assess whether or not the market will anticipate a change in the target rate by bidding up the federal funds rate ahead of the upcoming FOMC meeting – a phenomenon called “front-running.”

Fed watchers will certainly want to follow these new binary options and consider using them to supplement any FOMC probabilities they currently calculate using the established fed funds futures or options contracts. Click here for more detail on how to use the new binary options to estimate FOMC probabilities.

### Recovering Probabilities from Binary Option Prices

Prices for the new binary option are quoted on the basis of a par of 100 points. Given that the contract pays $1,000 for positions that finish in the money, this implies that one price point is equivalent to $10 and that an option’s price can never be greater than 100. At the same time, an option’s price can never fall below zero since the option does not have to be exercised if it finishes out of the money. The fact that prices are bounded between 0 and 100 means that the contract has been designed to closely conform to probabilities, making for an easy interpretation of the prices of binary options and an easy recovery of target rate probabilities.

As an example, consider the prices for binary options on the October 2006 contract quoted on July 14, 2006. The call with a strike price of 94.50 had a settlement price of 43, while the put with the same strike price had a settlement price of 24. The call with a strike of 94.50 only pays off if 100 minus the target rate chosen at the October meeting is above 94.50 – that is, it only pays off if the FOMC chooses a target rate below 5.50 percent. The put with a strike of 94.50 only pays off if 100 minus the target rate chosen at the October meeting is below 94.50 – that is, it only pays off if the FOMC chooses a target rate above 5.50 percent.

Ignoring discounting, the price of the call of 43 directly translates into the probability that the target rate chosen at the October FOMC meeting will be below 5.50 percent. This is the case since the call will pay the same amount no matter how far it is in the money. The call will pay $1,000 whether the FOMC chooses a target rate of 5.25, 5.00, or 4.75 percent. Similarly, the price of the put of 24 directly translates into the probability that the target rate chosen at the October FOMC meeting will be above 5.50 percent. The put will pay $1,000 whether the FOMC chooses a target rate of 5.75, 6.00, or 6.25 percent.

In short, and ignoring discounting, the binary call option prices give the probability that the FOMC will choose a target rate that is below 100 minus the strike price, and binary put option prices give the probability that the FOMC will choose a target rate that is above 100 minus the strike price.

Making an assumption about the possible target rates from which the FOMC will choose at the upcoming meeting then allows for a recovery of the probability associated with each of the assumed choices. Continuing with the example, as of July 14, 2006, the target federal funds rate was 5.25 percent. Suppose that an analyst believes that at the October meeting the FOMC will choose from only three possible target rates—5.25, 5.50, and 5.75 percent.

With this assumption, the price of 43 for the call option with a strike price of 94.50 tells us that the probability of the FOMC choosing a target rate of 5.25 percent is 43 percent, since 5.25 is the only assumed target rate choice that is below 5.50 (100 minus 94.50) percent. The price of 24 for the put option with a strike price of 94.50 tells us that the probability of the FOMC choosing a target rate of 5.75 percent is 24 percent, since 5.75 is the only assumed target rate choice that is above 5.50 (100 minus 94.50) percent.. The probability for the third choice, a target rate of 5.50 percent, must then be 33 percent, since the probabilities of the three assumed choices must sum to 100 percent.

Of course, it is interesting to consider alternative assumptions for the possible target rates that will be selected at the October FOMC meeting. Perhaps the FOMC will choose from four target rates, or perhaps from only two. Moreover, more than two options are actively traded - it seems desirable to use all the available information when assessing target rate probabilities. The work of Carlson, Craig, and Melick (2005) provides an easy–to-implement method for estimating target rate probabilities under a variety of assumptions and using more than two option prices.

Click here to examine an Excel spreadsheet that implements their technique for all the data available on July 14, 2006, under three different assumptions of possible target rate choices available to the FOMC in October 2006. Each assumption is a separate worksheet/tab in the spreadsheet, and estimates for the probabilities are presented using both an unrestricted estimator and a restricted estimator that forces the probabilities to sum to one.

It is reassuring that the spreadsheet returns the same probabilities as those calculated in the above example using only two option prices, when it is assumed that the FOMC will choose from 5.25, 5.50, and 5.75 percent at the October meeting. Notice also that the assumption that the FOMC will choose from only two target rates in October seems to be a poor assumption, as indicated by the large difference between the unrestricted and restricted estimators.

To be completely correct, option prices should be adjusted for discounting when estimating probabilities, since the option prices are valuing a payoff in the future. This is simple to do, but makes little difference, because the binary contracts only cover the next four FOMC meetings, and the interest rates involved in the discounting are relatively small. Details on implementing the discounting can be found in Carlson, Craig, and Melick (2005).

### References

Carlson, John B., Ben R. Craig, and William R. Melick (2005) “Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures,”*Journal of Futures Markets*25(12), December, pp.1203-1242.